What is the Greatest Common Factor of 7290 and 7305?

Greatest common factor (GCF) of 7290 and 7305 is 15.

GCF(7290,7305) = 15

We will now calculate the prime factors of 7290 and 7305, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7290 and 7305.

How to find the GCF of 7290 and 7305?

We will first find the prime factorization of 7290 and 7305. After we will calculate the factors of 7290 and 7305 and find the biggest common factor number .

Step-1: Prime Factorization of 7290

Prime factors of 7290 are 2, 3, 5. Prime factorization of 7290 in exponential form is:

7290 = 2¹ × 3⁶ × 5¹

Step-2: Prime Factorization of 7305

Prime factors of 7305 are 3, 5, 487. Prime factorization of 7305 in exponential form is:

7305 = 3¹ × 5¹ × 487¹

Step-3: Factors of 7290

List of positive integer factors of 7290 that divides 7290 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 90, 135, 162, 243, 270, 405, 486, 729, 810, 1215, 1458, 2430, 3645

Step-4: Factors of 7305

List of positive integer factors of 7305 that divides 7290 without a remainder.

1, 3, 5, 15, 487, 1461, 2435

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7290 and 7305. The biggest common factor number is the GCF number.
So the greatest common factor 7290 and 7305 is 15.

Also check out the Least Common Multiple of 7290 and 7305